BOOLEAN ALGEBRA

Development of Boolean Algebra

Ages before well known mathematicianAristotleconstructed a system of lining out the formal logic and wrote six theses on it adding a great value to human reasoning. For centuries since then people have not been able to solve the problems using conventional tools of maths, until George Boole did it. He manipulated these computations easily to arrive at a solution using his very own conventional tools of math. This work was published in 1854 which resulted in the development of a completely new system, the algebra of logic or commonly called the “BOOLEAN ALGEBRA.”

Binary Valued Quantities

Every day we, the human are making some or the other logical decisions involving reasoning. E.g. “Should I carry the book or not?”, “Should I use the mobile or not?” all of these questions requires an answer, YES or NO, with proper reasoning. This shows that the basic Boolean Algebra is also applicable in our day to day lives as a matter of reasoning. This decision of YES or NO is known as the Binary Decision. And each of the above decision is a binary decision.

Some more examples:

1. Indira Gandhi was the only woman Prime minister of India.

2. 15 - 6 = 9

3. Delhi is the biggest state in India.

4. What did you just say?

5. What you did yesterday?

1stand 2ndare TRUE but 3rdif FALSE; 4thand 5thare questions which cannot be answered in YES or NO, TRUE or FALSE.

Thus the sentences which can be considered TRUE or FALSE, YES or NO are called the logical statements. This Yes or No is depicted by binary values 1 and 0 respectively.

Truth Table And Its Application

The most basic thing about Boolean algebra is the knowledge of Truth Table. Truth table is a table which represents the maximum possible value of logical variables/ statements grouped along all the possible outcomes of given combination.

For example, following can have only one of the two given values, (TRUE ( YES ) or FALSE ( NO )).

1. I want to have Coffee.

2. Coffee is readily available.

I want to have coffee.

T

T

F

F

Coffee is readily available.

T

F

T

F

(Result)I’ll have coffee.

T

F

F

F

Now we can represent the following in form of binary values.

X

Y

R

1

1

1

1

0

0

0

1

0

0

0

0

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